In the square artificial spin ice, which was first investigated in [1]}, four spins are meeting in each lattice vertex. Because of the dipole-dipole interactions, it is advantageous for the neighboring spins to line up “head-to-tail”, so the ground states configurations will obey to the so-called “ice rule” when two spins point into the vertex and other two spins point out. That is, if one denote the head of the magnetization vector of each islands for “\(+\) ” and the tail for “\(-\) ” and sum them at each vertex of the lattice, we get dumbbell magnetostatic charge model [2]}, [3]}. If any vertex has a non zero charge, then this means some excitation in this area.
